To represent potential DOAs, the unit half sphere is discretized using 1321 points obtained by subdividing a 20-sided convex polyhedron [1]}, giving a solid angle of approximately \(3^{\circ }\)  between grid points.
A set of time difference of arrival (TDOAs) matches each DOA based on the microphone array geometry and speed of sound (assuming plane waves).
For each hypothetical DOA \(i\) , ODAS computes SRP-PHAT, with power \(E_i\)[2]}:
\(E_i = \sum _{p=1}^{7} \sum _{q=p+1}^{8} \frac{1}{N} \sum _{k=0}^{N-1}{\frac{X_p[k] X^*_q[k]}{|X_p[k]||X_q[k]|} \exp {\left(j\frac{2\pi \tau _{i,p,q} k}{N}\right)}},\) 
